Quadratic polynomials in practice

The following exercises are solved in this step.

We invite you to try to solve them before watching the video.

In any case, you will find below a PDF file with the solutions.

Exercise 1.

Write the following polynomials in the form (a(x+p)(x+q)):

i) (2x^2+4x-30);

ii) (3x^2+7x-6).

Exercise 2. [Solved only in the PDF file]

Compute the roots of the polynomial (4x^2+7x-12).

Exercise 3. [Solved only in the PDF file]

Do the graphs of (f) and (g) intersect, if

i) (f:xmapsto x^2-3x+7) and (g:xmapsto 2x-3)?

ii) (f:xmapsto x^2-3x+7) and (g:xmapsto 2x+13)?

Exercise 4. [Solved only in the PDF file]

Determine the maximum value of (-2x^2+3x-7).